Home
Class 11
MATHS
Prove that: |costhetacos(60^0-theta)cos(...

Prove that: `|costhetacos(60^0-theta)cos(60^0+theta)lt=1/4` for all values of `thetadot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS OF COMPOUND ANGLES

    RD SHARMA ENGLISH|Exercise All Questions|149 Videos

Similar Questions

Explore conceptually related problems

Prove that: |sintheta."sin"(60-theta).sin(60+theta)|lt=1/4 for all values of theta .

Prove that: cos Acos(60^0-A)cos(60^0+A)=1/4cos3A

If A=cos^2theta+sin^4theta, prove that 3/4lt=Alt=1 for all values of thetadot

Prove that: 4\ costhetacos\ (pi/3+theta)cos(pi/3-theta)=cos3theta

Prove that: t a nthetatan(60^0-theta)tan(60^0+theta)=tan3thetadot

Prove that sin theta sin(60^(@)-theta) sin(60^(@)+theta)=1/4 sin3theta .

Prove that 1-cos^(2)theta-sin^(2)theta=0

Prove that: a) cotthetacot(60^(@)-theta)cot(60^(@)+theta)=cot3theta b) cos5theta=16cos^(5)theta-2thetacos^(3)theta+5costheta c) sin4theta=4sinthetacos^(3)theta-4costhetasin^(3)theta

Prove that : cos Acos(60-A)cos(60+A)=1/4cos3A

Prove that: tantheta.tan(60^0-theta).tan(60^0+theta)=tan3thetadot.'

RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-All Questions
  1. Prove the following identity: cot A+cot(60^0+A)+cot(120^0+A)=3cot3A

    Text Solution

    |

  2. Prove that: sin^3A+sin^3((2pi)/3+A)+sin^3((4pi)/3+A)=-3/4sin3Adot

    Text Solution

    |

  3. Prove that: |costhetacos(60^0-theta)cos(60^0+theta)lt=1/4 for all valu...

    Text Solution

    |

  4. Prove that: sin(pi/5) sin2pi/5 sin3pi/5 sin4pi/5=5/16

    Text Solution

    |

  5. Prove that cos((2pi)/(15))cos((4pi)/(15))cos((8pi)/(15))cos((16pi)/(15...

    Text Solution

    |

  6. Prove that: sin 12^0sin 48^0sin 54^0=1/8dot

    Text Solution

    |

  7. The value oif the expressin (1+cospi/10)(1+cos(3pi)/10)(1+cos(7pi)/10)...

    Text Solution

    |

  8. Prove that ; 4 sin 27^@=(5+sqrt(5))-sqrt((3-sqrt(5))) we have

    Text Solution

    |

  9. Prove that : sin^2(72^@) - sin^2 (60^@) = (sqrt5 - 1)/8

    Text Solution

    |

  10. Prove that: sin^2 24^0-sin^2 6^0=(sqrt(5)-1)/8

    Text Solution

    |

  11. Prove that: sin^2 42^0-cos^2 78^0=(sqrt(5)+1)/8

    Text Solution

    |

  12. Prove that: cos 78^0cos 42^0cos 36^0=1/8

    Text Solution

    |

  13. Show that cos(pi/15)cos((2pi)/15)cos((3pi)/15)cos((4pi)/15)cos((5pi)/1...

    Text Solution

    |

  14. Prove that cos6^@ . cos42^@. cos66^@ cos78^@= 1/16

    Text Solution

    |

  15. Prove that: sin6^0sin42^0sin 66^0sin 78^0=1/(16)

    Text Solution

    |

  16. Prove that: sin36^0s in 72^0s in 108^0s in 144^0=5/(16)dot

    Text Solution

    |

  17. If cos4x=1+ksin^2x cos^2x , then write the value of kdot

    Text Solution

    |

  18. If tanx/2=m/n ,\ then write the the value of msinx+n\ cos xdot

    Text Solution

    |

  19. If pi/2 < theta < (3pi)/2 then write the value of sqrt((1+cos2theta)...

    Text Solution

    |

  20. If pi/2<theta<pi,then write the value of sqrt(2+sqrt(2+2cos2theta)) in...

    Text Solution

    |